"I consider Hillary a strong friend," Obama said during an interview with CBS' "60 Minutes" that aired Sunday.
"Very warm, close," said Clinton, who will be leaving her post soon.
They brushed off the tough primary battles their campaigns waged five years ago as the result of trying to draw differences between them when there really wasn't any, they said during the interview taped last week.
"Despite our hard-fought primary, we had such agreement on what needed to be done for our country," Clinton said.
"Made for tough debates, by the way," Obama said, "because we could never figure out what we were different on."
The campaign rivalry was set aside, however, when Obama nominated Clinton as his top diplomat, changing the dynamics between the two.
"What did evolve was a friendship, as opposed to just a professional relationship," Obama said. "Friendships involve a sense of trust and being in the foxhole together. And that emerged during the course of months when we were making some very tough decisions."
Obama defended himself against comments that he has been passive on the world stage, noting his intervention in Libya, where a revolution aided by NATO air support led to the death of the country's longtime dictator, Moammar Gadhafi.
"Moammar Gadhafi probably does not agree with that assessment," Obama said, "or at least if he was around, he wouldn't agree with that assessment."
Obama and Clinton discouraged reading anything into the interview about the 2016 presidential election, when many Democrats expect Clinton to seek the nomination again.
"You guys in the press are incorrigible," Obama said during the "60 Minutes" interview. "I was literally inaugurated four days ago, and you're talking about elections four years from now."
"I am still secretary of state," Clinton said, "so I'm out of politics. And I'm forbidden from even hearing these questions."